Start with C!
When I installed Linux three years ago I began to learn bash (the most common shell language used in nix) and a little bit of C. That helped me to understand the way computers work more than anything else I had experienced in the previous 20 years. (not that I tried that hard)

I have really gotten into C for the last nine months and continue to learn. I compile on in windows now too using the GNU MINGW compiler which works much like Linux's GNU C (gcc). I found that many other languages are acutally written in C! Understanding C will make it that much easier to learn any other programming language.

I have had a couple of occasions to use a little C++, but haven't found C lacking enough to make me want to move in that direction yet. I am presently moving into using C for win32 API and still find no need for C++. There will probably come a time though... Ain't there yet...
Howard;

It all depends on your requirement and so you should have some focus which should be the base of your decision but I would say you should be going with C++ beacuse that will help you get into some of the latest technolgy like Java or DotNet